Texture not going on to Model
A couple of things:

Your TowerTexture.png file is very small --  4 pixels x 2 pixels -- and was not assigned as the material's texture. More on that in a moment, but here is how you can see the size of your texture file:
 

I took the .blend file you uploaded and did a couple of things: I unwrapped the tower and applied a color grid as an image texture. This is a feature you can use within Blender to add a numbered grid as a new image texture:



I also made the new image 1024 x 1024, which is a standard size... but you can use larger or smaller.... It helps to size them as pow3ers of 2, like computer RAM:  512, 1024, 2048, 4096. 4096 would be pretty big... but I am just showing you the powers of 2. This is not mandatory, but speeds rendering.

I then applied the color grid file to your model:



The numbered grid lets you see if your texture file is being squashed or stretched... There are a couple of ways to deal with scaling your image, but here is one:


I also turned your lamp into a "sun" type lamp and pulled the camera further back to get a full view of the tower. I am not sure those changes were critical, but I wanted to note that I did this. I uploaded the file with these changes and you can download it below.

Also, when you are assigning an image to a material in Blender Internal, specify "Image or Movie" in the texture "Type" dropdown:


Then select the file to wrap onto your model. But make sure you are specifying that the image is applied as a material texture here --



I believe you had accidentally assigned it as a brush texture (the checkered box to the right of the material box...)

Anyway, once you see the color grid in place, you can replace it with the real texture you want to use.... And you can make your tower more than on material and image texture, but I hope this helps.